TY - JOUR

T1 - The Set of Linear Time-Invariant Unfalsified Models with Bounded Complexity is Affine

AU - Mishra, Vikas Kumar

AU - Markovsky, Ivan

PY - 2020

Y1 - 2020

N2 - We consider exact system identification in the behavioral setting: given an exact (noise-free) finite time series, find the set of bounded complexity linear time-invariant systems that fit the data exactly. First, we modify the notion of the most powerful unfalsified model for the case of finite data by fixing the number of inputs and minimizing the order. Then, we give necessary and sufficient identifiability conditions, i.e., conditions under which the true data generating system coincides with the most powerful unfalsified model. Finally, we show that the set of bounded complexity exact models is affine: every exact model is a sum of the most powerful unfalsified model and an autonomous model with bounded complexity.

AB - We consider exact system identification in the behavioral setting: given an exact (noise-free) finite time series, find the set of bounded complexity linear time-invariant systems that fit the data exactly. First, we modify the notion of the most powerful unfalsified model for the case of finite data by fixing the number of inputs and minimizing the order. Then, we give necessary and sufficient identifiability conditions, i.e., conditions under which the true data generating system coincides with the most powerful unfalsified model. Finally, we show that the set of bounded complexity exact models is affine: every exact model is a sum of the most powerful unfalsified model and an autonomous model with bounded complexity.

UR - http://www.scopus.com/inward/record.url?scp=85098782668&partnerID=8YFLogxK

U2 - 10.1109/TAC.2020.3046235

DO - 10.1109/TAC.2020.3046235

M3 - Article

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

ER -